I recently watched a lesson about this and so many kids were confused. The teacher said sweets were discrete and also books. However, the students said you could have all sorts of sweet sizes if a sweet broke so wouldn't it be continuous. The same with ripped books that were still being used but the book is in two halves or 1/4 and 3/4 etc.
Even shoe size was quetioned as of places that customize shoes for you so you get a more accurate size and not the usual discrete shoe sizes that we are used to.
What I'm looking for is good examples for discrete data. I thought discrete could be living humans as I can only think of students saying you can be half dead which I could explain how that isn't really measurable.